Now we show that the accessibility assumption in Theorem REF 
implies condition REF  in Theorem REF . We use the result from [1]} that partially hyperbolic, volume preserving center bunched diffeomorphism is ergodic. By condition (1) in Theorem REF , the generic singular element is accessible partially hyperbolic diffeomorphism. By Lemma REF , it is also center bunched. This implies ergodicity for the generic singular element in \(\rm Ker \lambda \) , which implies directly REF .
